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Author ORCID Identifier
https://orcid.org/0009-0001-6050-7263
Date Available
5-6-2028
Year of Publication
2026
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Statistics
Faculty
Derek Young
Abstract
The dissertation focuses on the problem about directional statistics. Directional data has received increasing attention across a large number of scientific fields. In particular, such data assume a notion of an underlying circular distribution, which is characterized by some form of angular or degree direction. Naturally, modeling with such distributions when observed covariates are present necessitate the use of regression methods. However, circular variables have some specific characteristics which are different from linear variables, so traditional linear models need an appropriate transformation to become circular models. This paper extends the simple circular-circular regression model and the circular-linear model into multiple circular-circular regression models, and models based on both circular and linear covariates. We further develop a degree determination algorithm that is used in the aforementioned models. This algorithm makes use of classic dimension reduction methods (principal component analysis and partial least squares) applied to multiple circular regression models. Performance of our methods are investigated and compared based on both simulated and real datasets. In the second part of the dissertation, we investigate the use of classical nonparametric tests for directional data, including the Watson–Williams test, the Mardia–Wheeler–Watson test, and several spacing frequency–based procedures. We further evaluate empirical power under multiple comparison adjustments such as Bonferroni, Holm, Hochberg, and Šidák corrections. In the end, we address interval estimation by developing new parametric and nonparametric methodologies for constructing tolerance intervals for circular data. We derive coverage properties under the von Mises distribution and assess performance, through extensive simulation studies. The proposed methods are evaluated using both simulated and real datasets, including an analysis of automobile crash data from the Kentucky public website. Together, these contributions provide an important contribution for modern directional data analysis.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2026.270
Archival?
Archival
Recommended Citation
Chen, Pengyuan, "Extending Some Statistical Methodologies for the Analysis of Circular Data" (2026). Theses and Dissertations--Statistics. 85.
https://uknowledge.uky.edu/statistics_etds/85
